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Simplifying -8 + -10m + 3m2 = 2m2 + 3m + 8 Reorder the terms: -8 + -10m + 3m2 = 8 + 3m + 2m2 Solving -8 + -10m + 3m2 = 8 + 3m + 2m2 Solving for variable 'm'. Reorder the terms: -8 + -8 + -10m + -3m + 3m2 + -2m2 = 8 + 3m + 2m2 + -8 + -3m + -2m2 Combine like terms: -8 + -8 = -16 -16 + -10m + -3m + 3m2 + -2m2 = 8 + 3m + 2m2 + -8 + -3m + -2m2 Combine like terms: -10m + -3m = -13m -16 + -13m + 3m2 + -2m2 = 8 + 3m + 2m2 + -8 + -3m + -2m2 Combine like terms: 3m2 + -2m2 = 1m2 -16 + -13m + 1m2 = 8 + 3m + 2m2 + -8 + -3m + -2m2 Reorder the terms: -16 + -13m + 1m2 = 8 + -8 + 3m + -3m + 2m2 + -2m2 Combine like terms: 8 + -8 = 0 -16 + -13m + 1m2 = 0 + 3m + -3m + 2m2 + -2m2 -16 + -13m + 1m2 = 3m + -3m + 2m2 + -2m2 Combine like terms: 3m + -3m = 0 -16 + -13m + 1m2 = 0 + 2m2 + -2m2 -16 + -13m + 1m2 = 2m2 + -2m2 Combine like terms: 2m2 + -2m2 = 0 -16 + -13m + 1m2 = 0 Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + -13m + 16 + m2 = 0 + 16 Reorder the terms: -16 + 16 + -13m + m2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -13m + m2 = 0 + 16 -13m + m2 = 0 + 16 Combine like terms: 0 + 16 = 16 -13m + m2 = 16 The m term is -13m. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13m + 42.25 + m2 = 16 + 42.25 Reorder the terms: 42.25 + -13m + m2 = 16 + 42.25 Combine like terms: 16 + 42.25 = 58.25 42.25 + -13m + m2 = 58.25 Factor a perfect square on the left side: (m + -6.5)(m + -6.5) = 58.25 Calculate the square root of the right side: 7.632168761 Break this problem into two subproblems by setting (m + -6.5) equal to 7.632168761 and -7.632168761.Subproblem 1
m + -6.5 = 7.632168761 Simplifying m + -6.5 = 7.632168761 Reorder the terms: -6.5 + m = 7.632168761 Solving -6.5 + m = 7.632168761 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + m = 7.632168761 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + m = 7.632168761 + 6.5 m = 7.632168761 + 6.5 Combine like terms: 7.632168761 + 6.5 = 14.132168761 m = 14.132168761 Simplifying m = 14.132168761Subproblem 2
m + -6.5 = -7.632168761 Simplifying m + -6.5 = -7.632168761 Reorder the terms: -6.5 + m = -7.632168761 Solving -6.5 + m = -7.632168761 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + m = -7.632168761 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + m = -7.632168761 + 6.5 m = -7.632168761 + 6.5 Combine like terms: -7.632168761 + 6.5 = -1.132168761 m = -1.132168761 Simplifying m = -1.132168761Solution
The solution to the problem is based on the solutions from the subproblems. m = {14.132168761, -1.132168761}
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